MIRD Dosimetry: Framework & Worked Examples

Quick Answer

The MIRD schema computes absorbed dose as D = Ã × S: the cumulated (time-integrated) activity à in a source region times the S-value (mean dose to a target per unit cumulated activity in the source). For a mono-exponentially clearing region, à = 1.443 × T_eff × A₀(region), where 1.443 = 1/ln2 and T_eff combines physical and biological half-lives. S-values come from anatomic models (OLINDA/EXM, MIRD pamphlets). Therapy dosimetry then respects organ-at-risk limits — classically ~2 Gy marrow, ~23 Gy kidney (BED), and lung limits for Y-90.

The Core Equation

Summed over all source regions:

• Ã = cumulated activity = ∫ A(t) dt (units: MBq·h or µCi·h) — the total number of decays in the source region.
• S = dose per unit cumulated activity (mGy/MBq·h) — encodes emission energy, geometry (absorbed fraction), and target mass.

Cumulated Activity (Ã) and Residence Time (τ)

For a region that takes up a fraction and clears mono-exponentially:

• 1.443 = 1/ln2 (the mean lifetime factor).
• T_eff combines the physical and biological half-lives:

• Residence time τ = Ã / A₀ (hours) — a normalized way to tabulate uptake.

Real kinetics are measured from serial imaging/blood sampling (multi-time-point SPECT/CT for Lu-177), fitting the time–activity curve and integrating it — the labor-intensive heart of patient-specific dosimetry.

The S-Value

• Δᵢ = mean energy emitted per decay for emission i.
• φᵢ = absorbed fraction (fraction of energy i deposited in the target).
• m_target = target mass.

For non-penetrating radiation (α, β), energy is deposited locally (self-dose φ ≈ 1 within the source; ≈ 0 to distant targets) — the reason β/α therapy dose is dominated by self-dose. For penetrating γ, φ < 1 and cross-organ doses matter. S-values are tabulated for reference phantoms and scaled to patient organ mass.

Worked Example 1 — Effective Half-Life & Cumulated Activity

A ¹⁷⁷Lu-DOTATATE administration; consider an organ with biological half-life 20 h for Lu-177 (physical T½ = 6.65 d = 159.6 h):

1. 1/T_eff = 1/159.6 + 1/20 = 0.00627 + 0.0500 = 0.0563 h⁻¹ → T_eff = 17.8 h.
2. If the organ's peak activity A₀(region) = 500 MBq: Ã = 1.443 × 17.8 h × 500 MBq = 12,843 MBq·h.
3. Residence time τ = Ã / A₀ = 1.443 × T_eff = 25.7 h.

The biological clearance dominates T_eff here — a physically long-lived nuclide can deliver far less dose than its physical half-life implies when biological clearance is fast (see effective half-life).

Worked Example 2 — Organ Absorbed Dose

Using à from above and a (illustrative) organ S-value = 0.15 mGy/(MBq·h):

D = Ã × S = 12,843 MBq·h × 0.15 mGy/(MBq·h) ≈ 1,930 mGy ≈ 1.9 Gy.

Add contributions from other source regions (cross-dose) via their Ã × S(target ← source) terms for the total organ dose. In practice, software (OLINDA/EXM, patient-specific voxel dosimetry) performs the summation across the reference phantom.

Organ-at-Risk Limits (Therapy)

Biologically effective dose (BED) corrects absorbed dose for dose rate and repair — important because a given Gy delivered slowly (radionuclide therapy) differs biologically from the same Gy delivered acutely (external beam). This is why kidney tolerance is expressed as BED for PRRT.

Patient-Specific vs Fixed-Activity

Most therapy is delivered at fixed/empiric activity (e.g. 7.4 GBq Lu-177-DOTATATE × 4; 200 mCi I-131). Dosimetry-guided dosing — serial SPECT/CT (or I-124 PET), time–activity fitting, S-value/voxel dose — is used where the therapeutic ratio is tight (extensive disease, renal impairment, pediatrics) and is an active area (personalized dosimetry improved Y-90 outcomes in DOSISPHERE-01).

Board-Level Synthesis

D = Ã × S. Cumulated activity à = 1.443 × T_eff × A₀(region) (1.443 = 1/ln2); T_eff combines physical and biological half-lives; the S-value = mean-energy × absorbed-fraction ÷ target mass. Sum Ã × S over all source regions for the total organ dose.

For α/β (non-penetrating) emitters, dose is dominated by self-dose (absorbed fraction ≈ 1 within the source; ≈ 0 at distance); for γ, cross-organ dose matters. This is the physical reason particle emitters are therapeutic and γ emitters are for imaging.

Therapy respects organ-at-risk limits — ~2 Gy marrow, ~23 Gy kidney (BED), and Y-90 lung limits — expressed where relevant as BED to account for dose rate and repair (a radionuclide-therapy Gy is not an external-beam Gy). Most therapy is fixed-activity; patient-specific dosimetry (serial SPECT/CT, OLINDA/voxel methods) is reserved for tight-therapeutic-ratio settings.

Related Pages

• Physics: Physics of nuclear medicine (effective half-life, LET), dosimetry & theranostics.
• Therapy: the radionuclide-therapy pages (Lu-177-DOTATATE/PSMA, I-131, Y-90).
• Calculators: decay, dosimetry, effective dose.

Figure / Diagram Suggestions

• A D = Ã × S schematic (time–activity curve → cumulated activity → S-value → dose).
• A self-dose vs cross-dose absorbed-fraction diagram (β/α vs γ).
• An organ-at-risk limits panel (marrow/kidney/lung with BED note).

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